Explicit solution for a Stefan problem with variable latent heat and constant heat flux boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Nieves Salva, Natalia^2,3  Alberto Tarzia, Domingo^1,2 

[1] Univ Austral, FCE, Dept Matemat, RA-1950 Rosario, Santa Fe, Argentina

[2] Consejo Nacl Invest Cient & Tecn, RA-1033 Buenos Aires, DF, Argentina

[3] Ctr Atom Bariloche, TEMADI, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina

关键词: Stefan problem;    Free boundary problem;    Explicit solution;    Similarity solution;    Sediment delta;   

DOI  :  10.1016/j.jmaa.2010.12.039

来源: Elsevier

【 摘 要 】

In Voller, Swenson and Paola [V.R. Voller, J.B. Swenson, C. Paola, An analytical solution for a Stefan problem with variable latent heat, Int. J. Heat Mass Transfer 47 (2004) 5387-5390], and Lorenzo-Trueba and Voller [J. Lorenzo-Trueba, V.R. Voller, Analytical and numerical solution of a generalized Stefan problem exhibiting two moving boundaries with application to ocean delta formation, J. Math. Anal. Appl. 366 (2010) 538-549], a model associated with the formation of sedimentary ocean deltas is studied through a one-phase Stefan-like problem with variable latent heat. Motivated by these works, we consider a two-phase Stefan problem with variable latent of fusion and initial temperature, and constant heat flux boundary conditions. We obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary problem for a semi-infinite material. Moreover, the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity. (C) 2010 Elsevier Inc. All rights reserved.

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